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Bifurcation at complex instability
Ollé Torner, Mercè; Pfenniger, Daniel
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
In an autonomous Hamiltonian system with three or more degrees of freedom, a family of periodic orbits may become unstable when two pairs of characteristic multipliers coallesce on the unit circle at points not equal to ±1, and then move off the unit circle. This paper develops normal forms suitable for the neighbourhood of such an, instability, and, at this approximation, demonstrates the bifurcation from the periodic orbit of a family of invariant two-dimensional tori. The theory is illustrated with numerical computations of orbits of the planar general three-body problem.
Differential equations
Global analysis (Mathematics)
Hamiltonian dynamical systems
Lagrangian functions
complex inestability
Equacions diferencials ordinàries
Varietats (Matemàtica)
Hamilton, Sistemes de
Lagrange, Funcions de
Classificació AMS::58 Global analysis, analysis on manifolds
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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